If the parent is completely inbred, with all genetic loci homozygous (both copies of a particular gene are the same), they will produce identical offspring.
Each offspring will one have a single choice for each gene it receives from each gamete from the single parent.

Otherwise, there will be genetic differences in the offspring.
If the parent is not homozygous at each loci, then each offspring will be randomly assigned (at fertilization) one of two different copies of each gene, from the single parent.
With many offspring, genetic differences will arise.

However, if this process is repeated for many generations, different copies of genes will gradually be lost, through random inbreeding processes.
This can lead to clonal or virtually clonal populations, such as this hermaphroditic killifish.
So after that happens, the answer would be yes.